No, the old address will always remain related to your wallet and may be used at any time. It’s just a security thing that Daedalus recommends you to accept each new incoming money onto new address, but you don’t have to. The only thing to remember is that when you send some coins, and you have a change - change will be automatically sent to a new address. But the previous one still may be used (but not recommended by Daedalus).
UPD: And also you don’t have to do anything extra if Daedalus creates you a new address - it all will be processed automatically, and all used addresses will remain active even if you completely delete your Daedalus and then install it again. Or even if you restore your wallet on another computer. Just be sure to store your 12 words.
You can read this comment, to find more detailed info about how addresses work in a wallet: